Question

1. in the figure below, ∠ace measures 130° and (overline{cb}) bisects ∠acd. what is the measure of ∠bcd? a. 15° b. 25° c. 40° d. 50°

Explanation:

Step1: Find ∠ACD

Since ∠ACE + ∠ACD = 180° (linear - pair of angles), and ∠ACE = 130°, then ∠ACD=180° - 130° = 50°.

Step2: Use the angle - bisector property

Since $\overline{CB}$ bisects ∠ACD, by the definition of an angle - bisector, ∠BCD=$\frac{1}{2}$∠ACD. Substituting ∠ACD = 50° into the formula, we get ∠BCD = $\frac{50^{\circ}}{2}=25^{\circ}$.

Answer:

B. 25°